If you have the same owner on several objects in several databases, and you have some stored procedure that access these objects, you don’t need to GRANT access permission to every object that the procedure needs to access. If the procedure and the objects have the same owner, you can to GRANT permission on the procedure and Database Engine will allow the procedure to access all other objects that share the same owner.
In this example, I will create two databases that have the same owner and a login that will be used to access the data. One database will have some table and other database will have a stored procedure that reads data from the table in other database. Login will be granted to execute the stored procedure, but not to read data from the table:
“Can” and “should” here probably have different answers. Far better to set up certificates for granting rights.